Toward a Constraint-Based Formalism of Physical Theories

This paper presents a first mathematical formalization of a constraint-based framework for physical theories. Physical theories are represented as structured objects consisting of states, observables, and dynamical laws. Constraint operators are introduced to encode symmetry, causality, quantum, and dynamical requirements. The space of physically admissible theories is defined as the intersection of constraint-defined subsets, leading to a perspective in which physical laws emerge as consistency conditions rather than fundamental axioms. This work builds on a prior conceptual study and provides a foundation for further development of a unified constraint-based formulation of physics.